# aperture2gain

Convert effective aperture to gain

## Syntax

``GdB = aperture2gain(A,lambda)``

## Description

example

````GdB = aperture2gain(A,lambda)` returns the antenna gain `GdB` corresponding to an effective aperture `A` for an incident electromagnetic wave with wavelength `lambda`. ```

## Examples

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An antenna has an effective aperture of 3 square meters. Find the antenna gain when used to capture an electromagnetic wave with a wavelength of 10 cm.

`g = aperture2gain(3,0.1)`
```g = 35.7633 ```

## Input Arguments

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Antenna effective aperture, specified as a positive scalar or as an N-element real-valued vector of positive values. If `A` is a vector, each element of `A` corresponds is the effective aperture of a different antenna. See Gain and Effective Aperture for a discussion of aperture and gain. Units are in square meters.

Data Types: `double`

Wavelength of the incident electromagnetic wave, specified as a positive scalar. The same wavelength applies to all antennas in `A`. The wavelength of an electromagnetic wave is the ratio of the wave propagation speed to the frequency. Units are in meters.

Data Types: `double`

## Output Arguments

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Antenna gain, returned as a scalar or as an N-element real-valued vector. The elements of `GdB` represent the gain corresponding to the elements in `A`. The size of `GdB` equals the size of `A`. Units are in dBi.

Data Types: `double`

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### Gain and Effective Aperture

The effective aperture describes how much energy is captured by an antenna from an incident electromagnetic plane wave. The effective area of the antenna and is not the same as the actual physical area. The array gain of an antenna G is related to its effective aperture Ae by:

`$G=\frac{4\pi }{{\lambda }^{2}}{A}_{e}$`

where λ is the wavelength of the incident electromagnetic wave. For a fixed wavelength, the antenna gain is proportional to the effective aperture. For a fixed effective aperture, the antenna gain is inversely proportional to the square of the wavelength.

The gain expressed in dBi (GdB) is

`$GdB=10{\mathrm{log}}_{10}G=10{\mathrm{log}}_{10}\left(\frac{4\pi {A}_{g}}{{\lambda }^{2}}\right).$`

The effective antenna aperture can be derived from the gain in dB using

`${A}_{e}={10}^{GdB/10}\frac{{\lambda }^{2}}{4\pi }.$`

 Skolnik, M. Introduction to Radar Systems, 3rd Ed. New York: McGraw-Hill, 2001.

 Richards, M. Fundamentals of Radar Signal Processing, New York: McGraw-Hill, 2005.